Mathematics, 15.05.2021 03:50, npellot123
The U. S. Department of Agriculture records data on farm acreage and number of farms by county for every county in the country. This takes considerable time and energy, and the results for each update (usually occurring approximately every five years) are a long time in process. A quicker way to update the data is by sampling. The table below shows the number of counties in each geographic region and a summary of farm acres (in thousands) for independent random samples of 22 counties from each region.
Region Number of counties
North Central 1052
North East 210
South 1376
West 418
Required:
a. Estimate the mean acreage for each region, with a margin of error.
b. Estimate the total acreage for each region, with a margin of error.
c. Estimate the difference between mean acreage for the North Central region and the South, with a margin of error.
d. Estimate the difference between mean acreage for the North East and the West, with a margin of error.
e. Estimate the mean acreage per county across the United States, with a margin of error.
Answers: 3
and then allocate the four regions of 
and 
.
, the 
for the value of 
which yields 
is given by :
![$n_1=n\left[\frac{N_1}{\sum_{K=1}^\mu N_K}\right]$](/tpl/images/1325/7812/98d8d.png)
![$=221\left[\frac{1052}{3056}\right]$](/tpl/images/1325/7812/f03ad.png)
![$n_2=n\left[\frac{N_2}{\sum_{K=1}^\mu N_K}\right]$](/tpl/images/1325/7812/2e702.png)
![$=221\left[\frac{210}{3056}\right]$](/tpl/images/1325/7812/bda70.png)
![$n_3=n\left[\frac{N_3}{\sum_{K=1}^\mu N_K}\right]$](/tpl/images/1325/7812/729b4.png)
![$=221\left[\frac{1376}{3056}\right]$](/tpl/images/1325/7812/96a08.png)
![$n_4=n\left[\frac{N_4}{\sum_{K=1}^\mu N_K}\right]$](/tpl/images/1325/7812/c0d77.png)
![$=221\left[\frac{418}{3056}\right]$](/tpl/images/1325/7812/01206.png)
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